Title:Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Abstract: Obtaining lower bounds for NP-hard problems has for a long time been an
active area of research. Recent algebraic techniques introduced by Jonsson et
al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$)
problem correlates to the lattice of strong partial clones. With this ordering
they isolated a relation $R$ such that SAT($R$) can be solved at least as fast
as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method
and show that such languages also exist for the max ones problem
(MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over
finite-valued constraint languages (VCSP($\Delta$)). With the help of these
languages we relate MaxOnes and VCSP to the exponential time hypothesis in
several different ways.

Comments:

This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 2014